Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:Let G be a k-edge-connected graph with gir...Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:Let G be a k-edge-connected graph with girth g. If $$ \alpha '(G) \leqslant ((k - 2)^2 + 2)\left\lfloor {\frac{g} {2}} \right\rfloor + \frac{{1 - ( - 1)^g }} {2}((k - 1)(k - 2) + 1) - 1, $$ where k = 1, 2, 3, and α′(G) denotes the edge independence number of G, then G is upper embeddable and the upper bound is best possible. And it has generalized the relative results.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10771062) New Century Excellent Talents in University (Grant No.NCET-07-0276)
文摘Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:Let G be a k-edge-connected graph with girth g. If $$ \alpha '(G) \leqslant ((k - 2)^2 + 2)\left\lfloor {\frac{g} {2}} \right\rfloor + \frac{{1 - ( - 1)^g }} {2}((k - 1)(k - 2) + 1) - 1, $$ where k = 1, 2, 3, and α′(G) denotes the edge independence number of G, then G is upper embeddable and the upper bound is best possible. And it has generalized the relative results.
